As a critical mental health disorder, depression has severe effects on both human physical and mental well-being. Recent developments in EEG-based depression analysis have shown promise in improving depression detection accuracies. However, EEG features often contain redundant, irrelevant, and noisy information. Additionally, realworld EEG data acquisition frequently faces challenges, such as data loss from electrode detachment and heavy noise interference. To tackle the challenges, we propose a novel feature selection approach for robust depression analysis, called Incomplete Depression Feature Selection with Missing EEG Channels (IDFS-MEC). IDFS-MEC integrates missing-channel indicator information and adaptive channel weighting learning into orthogonal regression to lessen the effects of incomplete channels on model construction, and then utilizes global redundancy minimization learning to reduce redundant information among selected feature subsets. Extensive experiments conducted on MODMA and PRED-d003 datasets reveal that the EEG feature subsets chosen by IDFS-MEC have superior performance than 10 popular feature selection methods among 3-, 64-, and 128-channel settings.
Electroencephalography (EEG) provides rich temporal information through multiple spatial channels, making it a valuable measure for depression analysis [1]. However, the large number of EEG channels often introduces redundant and noise features, which hinders the accuracy of EEG-based depression diagnosis. Feature selection is an effective strategy to address the issues by reducing dimensionality and enhancing interpretability.
Feature selection methods are generally categorized into filter, wrapper, and embedded approaches. Filter-based methods apply variable ranking techniques and carry a lower risk of overfitting [2]. However, filter methods may neglect inter-variable correlations, which often limits the effectiveness of the selected subsets [3]. Wrapper-based methods evaluate feature subsets based on classifier performance, offering higher accuracy at high computational cost [4]. Yet, they are often criticized for being computationally intensive and susceptible to overfitting [4]. Compared to filter and wrapper methods, embedded methods integrate feature selection within the model training process, improving efficiency while reducing redundancy [5]. Among embedded methods, orthogonal regression-based techniques could retain more discriminative and structural information in high-dimensional data [6].
Despite these advantages, the effectiveness of existing approaches is limited by incomplete EEG channel data which often caused by electrode detachment or transmission errors [7]. Channel loss occurs frequently in clinical depression detection due to the practical challenges of EEG acquisition [8]. As a result, channellevel data loss can weaken feature representativeness and reduce model accuracy especially in multi-channel EEG data, which ultimately compromising the reliability of depression diagnosis [9].
To address the problems, we propose a novel orthogonal regression based feature selection approach for robust depression analysis, called Incomplete Depression Feature Selection with Missing EEG Channels (IDFS-MEC). The main contributions are as follows:
• A novel method for depression identification with incomplete EEG channels: IDFS-MEC incorporates missingchannel indicator information and adaptive channel weight learning into orthogonal regression to handle incomplete channels. In addition, global redundancy minimization learning is applied to minimize redundancy among feature subsets.
• An efficient optimization strategy: An optimization algorithm integrates Generalized Power Iteration (GPI) [10] with general augmented Lagrangian multiplier(ALM) [11] to optimize objective function of IDFS-MEC.
• Vast empirical validation: Extensive experiments were pre-arXiv:2511.11651v1 [cs.LG] 10 Nov 2025 formed on the MODMA and PRED-d003 datasets across 3-, 64-, and 128-channels and the experimental results show that IDFS-MEC outperforms among ten advanced feature selection methods.
As shown in Fig. 1, raw EEG data with varying missing channels were processed to construct the EEG feature set. Adaptive channel weighting and weighted orthogonal regression were then applied, where missing-channel indicator information incorporated to reduce the impact of channel loss variability on feature selection. Global redundancy minimization learning is utilized to reduce redundant information among selected EEG feature subsets.
A global redundancy matrix R further minimized redundancy of features which can be computed with following expression:
where fi ∈ R n×1 and fj ∈ R n×1 represent column vectors corresponding to the i-th and j-th features (xi and xj), respectively. fi ∈ R n×1 and fj ∈ R n×1 are calculated using a centering matrix Z as follows:
in which In is the identity matrix and
To achieve effective feature selection with missing channels, the following objective function is constructed:
where ch indicates the channel number and v represents corresponding channel index. n, c, and d (v) are the number of samples, classes, and features per channel.
is a vector formed by the feature weights and matrix Θ (v) is the diagonalizing result of θ (v) .
By taking the partial derivative with respect to the bias term b (v) , setting it to zero, and substituting it back, the objective function of Eq. ( 3) could be reformulated as:
where
When Θ (v) and α (v) are fixed and irrelevant terms are omitted, the following function for W (v) can be written as:
GPI [10] can be employed to solve W (v) in Eq. (5).
When W (v) and α (v) are fixed and irrelevant terms are omitted, the following function for Θ (v) can be written as:
where
The subproblem indicator matrix S in Eq. ( 6) can be reformulated as:
where
Eq. ( 7) can be solved using ALM method [11].
When W (v) and Θ (v) are fixed and irrelevant terms are omitted, the following function for α (v) can be written as:
where
. This is a quadratic programming problem with a closed-form solution, which can be derived using the Karush-Kuhn-Tucker conditions and is given by:
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